XIII. The variation of molecular surface-energy with temperature

Abstract 1. The well-known relation of volume-energy to temperature, expressed by the equation pv = RT, and the simple relations between p, v, and T when the substance examined is in the state of gas, together with the constancy in the value of R, if the weights of unit volumes of gases taken are proportional to their molecular weights, have led us to make experiments on the surface-tension of liquids in the hope of discovering relations as direct and simple We were guided to this research by experiments by Eötvös, which shall, be discussed later.* We have not been disappointed; it appears that a similar formula expresses with moderate accuracy the variation of surface-energy with temperature; it may be stated in similar terms, using the symbols γ for surface-tension, i. e., the force exerted along a linear centimetre of the liquid ; s for a surface over which are distributed a number of molecules the same for all liquids; k for a constant analogous to R in the gaseous equation; and τ for temperature measured in Centigrade degrees downwards, the critical temperature being taken at zero. An equation completely analogous to the gaseous equation, pv = RT, should therefore be γs = kt. That this is reasonable follows from the following consideration :—In the gas equation, pv = RT, if v be kept constant, p decreases with fall of T, until where p = 0, T = — 273°, or absolute zero; the origin of the scale of absolute temperature is also the origin of the scale of pressure.